The landing field can in principle be extended to (sub-)manifolds \(\mathcal {M}\)  of \(\mathbb {R}^d\)  that are orientable(see e.g. [1]} and [2]}).
Indeed, one can derive a field \(G(x)\)  and a potential \(\mathcal {N}(x)\)  such that when \(x\in \mathcal {M}\) , \(G(x) = \operatorname{Grad}f(x)\) , such that \(\nabla \mathcal {N}(x)\)  is 0 if and only if \(x\in \mathcal {M}\) , and such that \(G(x)\)  and \(\nabla \mathcal {N}(x)\)  are always orthogonal. These properties are sufficient to obtain prop:stationnary.
However, these maps might not be tractable, while on \(\mathcal {O}_p\)  their expressions are simple and cheap to compute.
